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A361099
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a(n) = n + 2*binomial(n,2) + 3*binomial(n,3) + 4*binomial(n,4).
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2
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0, 1, 4, 12, 32, 75, 156, 294, 512, 837, 1300, 1936, 2784, 3887, 5292, 7050, 9216, 11849, 15012, 18772, 23200, 28371, 34364, 41262, 49152, 58125, 68276, 79704, 92512, 106807, 122700, 140306, 159744, 181137, 204612, 230300, 258336, 288859, 322012, 357942, 396800, 438741
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of ordered set partitions of an n-set into 2 sets such that the first set has either 3, 2, 1 or no elements, the second set has no restrictions, and an element is selected from the second set.
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LINKS
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FORMULA
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E.g.f.: (1 + x + x^2/2 + x^3/6)*x*exp(x).
O.g.f.: x*(1 - x + 2*x^2 + 2*x^3)/(1 - x)^5.
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EXAMPLE
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The 294 set partitions for n=7 are the following (where the element selected from the second set is in parentheses):
{ }, {(1),2,3,4,5,6,7} (7 of these);
{1}, {(2),3,4,5,6,7} (42 of these);
{1,2}, {(3),4,5,6,7} (105 of these);
{1,2,3}, {(4),5,6,7} (140 of these).
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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